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Optimization of Real-Time Systems with Deadline Miss Ratio Constraints

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1 Optimization of Real-Time Systems with Deadline Miss Ratio Constraints
Sorin Manolache, Petru Eles, Zebo Peng {sorma, petel, Linköping University, Sweden

2 Introduction Task execution times are not fixed
 stochastic task execution times Probabilistic behaviour and implicitly probabilistic guarantees Ratio of missed deadlines is an important indicator of system performance, obviously of stochastic nature  soft real-time systems Optimizing this indicator by means of mapping of tasks to processors and assignment of priorities to tasks  multiprocessor applications Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 2

3 Contribution Task mapping and priority assignment heuristic for deadline miss ratio minimization Performance analysis algorithm that obtains the deadline miss ratio per task for a given task mapping alternative driven by The heuristic is iterative and transformational The analysis algorithm is fast and sufficiently accurate Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 3

4 Outline Stochastic task execution times Problem formulation
Mapping heuristic Deadline miss ratio analysis Experimental results Conclusions Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 4

5 Stochastic execution times
Expensive hardware 0% missed deadlines Probability Task execution time Task execution time Probability Affordable hardware <5% missed deadlines Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 5

6 Problem formulation, input
Task graphs Task periods 2s 4s 6s 10s Processors, buses, interconnection Task execution time probability density functions Task execution time Probability Message transmission time probability density functions Task and task graph deadlines Deadline miss ratio thresholds miss 10% miss 2% miss 4% critical Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 6

7 Problem formulation, output
Task priority assignment 1 2 3 4 Task mapping such that devi is minimized, where mi is the deadline miss ratio of task ti and Ti is its deadline miss ratio threshold Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 7

8 Mapping heuristic Based on Tabu search [Glover, 1989]
At each iteration, an improvement of the cost function is sought by modifying the problem parameters (task mapping and/or task priority)—a move The reversed modification is kept tabu for a small number of iterations Thus, the heuristic is forced to exit local minima Cost function Problem parameters Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 8

9 Mapping heuristic Initial solution Determine candidate moves No Yes
Satisfied? Final solution Candidate moves Current solution Evaluate candidate move No All candidates evaluated? Yes Select best Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 9

10 Moves One move is performed every iteration
A move changes the mapping and/or the priority of exactly one task The “best” move is selected and leads to the next temporary solution At each step, there are N(N+P-2) move outcomes to evaluate (Exhaustive Neighbourhood search, ENS) N—number of tasks P—number of processors Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 10

11 RNS By intelligently selecting a subset of promising candidate moves, the search could be significantly sped up Restricted Neighbourhood Search (RNS) Tasks are ranked and only the moves operating on the top [N/2] tasks are considered For each selected task, the candidate processors are ranked and only the top 2 processors are considered RNS reduces the set of candidate moves at each iteration P times compared to ENS Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 11

12 Task ranking A B C E F D A B C E F D A B C E F A E F B … A C B … D 12
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 12

13 Deadline miss ratio analysis
Exact DMR analysis for monoprocessor systems [ECRTS 2001] Theoretically applicable to multiprocessor systems, however it becomes prohibitively expensive Faster and approximate analysis for multiprocessor systems [ICCAD 2002] However it is still too slow to be plugged into an optimization loop Analysis complexity is reduced by two means: Task start and finish times are approximated with discrete values Two types of dependencies between some random variables are neglected Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 13

14 Deadline miss ratio analysis
X Y Z A Y Z X Y Z X P(X>max(Y, Z)) = P(X>Y)  P(X>Z) Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 14

15 Deadline miss ratio analysis
B C A B C Time P(LC(t)) = P(LC(t)|AC<t) Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 15

16 Deadline miss ratio analysis
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 16

17 Experimental setup 396 randomly generated benchmarks
# of tasks ranging from 20 to 40 # of processors ranging from 3 to 8 Mapping and priority assignment with Exhaustive neighborhood search (ENS) Restricted neighborhood search (RNS) Comparison of cost function values and run times Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 17

18 Experimental results Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 18

19 Experimental results Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 19

20 LO-AET Laxity optimization based on average execution times of tasks
Why not Use average task execution times instead of task execution time probability density functions Optimize a performance indicator based on average task execution times, e.g. average laxity And hope that it will lead also to an optimal deadline miss ratio Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 20

21 Experimental results Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 21

22 Experimental results Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 22

23 Conclusions Task mapping and priority assignment heuristic for soft real-time applications with stochastic task execution times Fast analysis for approximation of task and task graph deadline miss ratios Average execution time based heuristics fall short of providing quality results Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng 23


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